LMFDB - Embedded newform 8015.2.a.l.1.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.48
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} +O(q^{10})$	\(q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} -1.80465 q^{10} -1.17911 q^{11} -2.38461 q^{12} -4.31155 q^{13} -1.80465 q^{14} +1.89741 q^{15} -4.93407 q^{16} -6.27501 q^{17} +1.08312 q^{18} -8.34549 q^{19} -1.25677 q^{20} +1.89741 q^{21} -2.12787 q^{22} -2.43958 q^{23} +2.54495 q^{24} +1.00000 q^{25} -7.78085 q^{26} +4.55345 q^{27} -1.25677 q^{28} -8.45454 q^{29} +3.42417 q^{30} +6.67107 q^{31} -6.22174 q^{32} +2.23725 q^{33} -11.3242 q^{34} +1.00000 q^{35} +0.754289 q^{36} -8.35200 q^{37} -15.0607 q^{38} +8.18079 q^{39} +1.34127 q^{40} +3.15447 q^{41} +3.42417 q^{42} -4.66888 q^{43} -1.48186 q^{44} -0.600181 q^{45} -4.40259 q^{46} +10.7388 q^{47} +9.36197 q^{48} +1.00000 q^{49} +1.80465 q^{50} +11.9063 q^{51} -5.41863 q^{52} +5.67308 q^{53} +8.21740 q^{54} +1.17911 q^{55} +1.34127 q^{56} +15.8348 q^{57} -15.2575 q^{58} +7.57294 q^{59} +2.38461 q^{60} -6.87376 q^{61} +12.0390 q^{62} -0.600181 q^{63} -1.35993 q^{64} +4.31155 q^{65} +4.03746 q^{66} -9.26226 q^{67} -7.88624 q^{68} +4.62889 q^{69} +1.80465 q^{70} -4.02518 q^{71} -0.805006 q^{72} -8.17594 q^{73} -15.0725 q^{74} -1.89741 q^{75} -10.4884 q^{76} +1.17911 q^{77} +14.7635 q^{78} -15.0772 q^{79} +4.93407 q^{80} -10.4403 q^{81} +5.69272 q^{82} +16.8700 q^{83} +2.38461 q^{84} +6.27501 q^{85} -8.42571 q^{86} +16.0418 q^{87} +1.58150 q^{88} -3.42934 q^{89} -1.08312 q^{90} +4.31155 q^{91} -3.06599 q^{92} -12.6578 q^{93} +19.3798 q^{94} +8.34549 q^{95} +11.8052 q^{96} -7.01775 q^{97} +1.80465 q^{98} -0.707676 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.80465	1.27608	0.638041	−	0.770002i	$-0.279745\pi$
$2$	1.80465	1.27608	0.638041	+	0.770002i	$0.279745\pi$
$3$	−1.89741	−1.09547	−0.547736	−	0.836651i	$-0.684510\pi$
$3$	−1.89741	−1.09547	−0.547736	+	0.836651i	$0.684510\pi$
$4$	1.25677	0.628385
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.42417	−1.39791
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.34127	−0.474211
$9$	0.600181	0.200060
$10$	−1.80465	−0.570681
$11$	−1.17911	−0.355514	−0.177757	−	0.984074i	$-0.556884\pi$
$11$	−1.17911	−0.355514	−0.177757	+	0.984074i	$0.556884\pi$
$12$	−2.38461	−0.688379
$13$	−4.31155	−1.19581	−0.597904	−	0.801568i	$-0.704000\pi$
$13$	−4.31155	−1.19581	−0.597904	+	0.801568i	$0.704000\pi$
$14$	−1.80465	−0.482314
$15$	1.89741	0.489910
$16$	−4.93407	−1.23352
$17$	−6.27501	−1.52191	−0.760956	−	0.648803i	$-0.775270\pi$
$17$	−6.27501	−1.52191	−0.760956	+	0.648803i	$0.775270\pi$
$18$	1.08312	0.255293
$19$	−8.34549	−1.91459	−0.957293	−	0.289120i	$-0.906637\pi$
$19$	−8.34549	−1.91459	−0.957293	+	0.289120i	$0.906637\pi$
$20$	−1.25677	−0.281022
$21$	1.89741	0.414050
$22$	−2.12787	−0.453664
$23$	−2.43958	−0.508687	−0.254343	−	0.967114i	$-0.581859\pi$
$23$	−2.43958	−0.508687	−0.254343	+	0.967114i	$0.581859\pi$
$24$	2.54495	0.519485
$25$	1.00000	0.200000
$26$	−7.78085	−1.52595
$27$	4.55345	0.876312
$28$	−1.25677	−0.237507
$29$	−8.45454	−1.56997	−0.784984	−	0.619516i	$-0.787329\pi$
$29$	−8.45454	−1.56997	−0.784984	+	0.619516i	$0.787329\pi$
$30$	3.42417	0.625166
$31$	6.67107	1.19816	0.599080	−	0.800689i	$-0.295533\pi$
$31$	6.67107	1.19816	0.599080	+	0.800689i	$0.295533\pi$
$32$	−6.22174	−1.09986
$33$	2.23725	0.389455
$34$	−11.3242	−1.94208
$35$	1.00000	0.169031
$36$	0.754289	0.125715
$37$	−8.35200	−1.37306	−0.686530	−	0.727101i	$-0.740867\pi$
$37$	−8.35200	−1.37306	−0.686530	+	0.727101i	$0.740867\pi$
$38$	−15.0607	−2.44317
$39$	8.18079	1.30998
$40$	1.34127	0.212074
$41$	3.15447	0.492645	0.246322	−	0.969188i	$-0.420778\pi$
$41$	3.15447	0.492645	0.246322	+	0.969188i	$0.420778\pi$
$42$	3.42417	0.528361
$43$	−4.66888	−0.711998	−0.355999	−	0.934486i	$-0.615859\pi$
$43$	−4.66888	−0.711998	−0.355999	+	0.934486i	$0.615859\pi$
$44$	−1.48186	−0.223399
$45$	−0.600181	−0.0894697
$46$	−4.40259	−0.649126
$47$	10.7388	1.56642	0.783208	−	0.621760i	$-0.213582\pi$
$47$	10.7388	1.56642	0.783208	+	0.621760i	$0.213582\pi$
$48$	9.36197	1.35128
$49$	1.00000	0.142857
$50$	1.80465	0.255216
$51$	11.9063	1.66721
$52$	−5.41863	−0.751428
$53$	5.67308	0.779258	0.389629	−	0.920972i	$-0.372603\pi$
$53$	5.67308	0.779258	0.389629	+	0.920972i	$0.372603\pi$
$54$	8.21740	1.11825
$55$	1.17911	0.158991
$56$	1.34127	0.179235
$57$	15.8348	2.09738
$58$	−15.2575	−2.00341
$59$	7.57294	0.985913	0.492957	−	0.870054i	$-0.335916\pi$
$59$	7.57294	0.985913	0.492957	+	0.870054i	$0.335916\pi$
$60$	2.38461	0.307852
$61$	−6.87376	−0.880095	−0.440047	−	0.897975i	$-0.645038\pi$
$61$	−6.87376	−0.880095	−0.440047	+	0.897975i	$0.645038\pi$
$62$	12.0390	1.52895
$63$	−0.600181	−0.0756157
$64$	−1.35993	−0.169992
$65$	4.31155	0.534782
$66$	4.03746	0.496977
$67$	−9.26226	−1.13157	−0.565783	−	0.824554i	$-0.691426\pi$
$67$	−9.26226	−1.13157	−0.565783	+	0.824554i	$0.691426\pi$
$68$	−7.88624	−0.956347
$69$	4.62889	0.557252
$70$	1.80465	0.215697
$71$	−4.02518	−0.477701	−0.238850	−	0.971056i	$-0.576771\pi$
$71$	−4.02518	−0.477701	−0.238850	+	0.971056i	$0.576771\pi$
$72$	−0.805006	−0.0948708
$73$	−8.17594	−0.956921	−0.478460	−	0.878109i	$-0.658805\pi$
$73$	−8.17594	−0.956921	−0.478460	+	0.878109i	$0.658805\pi$
$74$	−15.0725	−1.75214
$75$	−1.89741	−0.219095
$76$	−10.4884	−1.20310
$77$	1.17911	0.134372
$78$	14.7635	1.67164
$79$	−15.0772	−1.69632	−0.848161	−	0.529739i	$-0.822290\pi$
$79$	−15.0772	−1.69632	−0.848161	+	0.529739i	$0.822290\pi$
$80$	4.93407	0.551646
$81$	−10.4403	−1.16004
$82$	5.69272	0.628655
$83$	16.8700	1.85172	0.925859	−	0.377869i	$-0.123343\pi$
$83$	16.8700	1.85172	0.925859	+	0.377869i	$0.123343\pi$
$84$	2.38461	0.260183
$85$	6.27501	0.680620
$86$	−8.42571	−0.908567
$87$	16.0418	1.71986
$88$	1.58150	0.168588
$89$	−3.42934	−0.363510	−0.181755	−	0.983344i	$-0.558178\pi$
$89$	−3.42934	−0.363510	−0.181755	+	0.983344i	$0.558178\pi$
$90$	−1.08312	−0.114171
$91$	4.31155	0.451973
$92$	−3.06599	−0.319651
$93$	−12.6578	−1.31255
$94$	19.3798	1.99887
$95$	8.34549	0.856229
$96$	11.8052	1.20486
$97$	−7.01775	−0.712545	−0.356272	−	0.934382i	$-0.615952\pi$
$97$	−7.01775	−0.712545	−0.356272	+	0.934382i	$0.615952\pi$
$98$	1.80465	0.182297
$99$	−0.707676	−0.0711242
$100$	1.25677	0.125677
$101$	9.71131	0.966312	0.483156	−	0.875534i	$-0.339490\pi$
$101$	9.71131	0.966312	0.483156	+	0.875534i	$0.339490\pi$
$102$	21.4867	2.12750
$103$	14.7691	1.45524	0.727620	−	0.685981i	$-0.240627\pi$
$103$	14.7691	1.45524	0.727620	+	0.685981i	$0.240627\pi$
$104$	5.78296	0.567066
$105$	−1.89741	−0.185169
$106$	10.2379	0.994397
$107$	−3.85087	−0.372278	−0.186139	−	0.982523i	$-0.559597\pi$
$107$	−3.85087	−0.372278	−0.186139	+	0.982523i	$0.559597\pi$
$108$	5.72264	0.550661
$109$	−16.2827	−1.55960	−0.779801	−	0.626027i	$-0.784680\pi$
$109$	−16.2827	−1.55960	−0.779801	+	0.626027i	$0.784680\pi$
$110$	2.12787	0.202885
$111$	15.8472	1.50415
$112$	4.93407	0.466226
$113$	3.99030	0.375376	0.187688	−	0.982229i	$-0.439901\pi$
$113$	3.99030	0.375376	0.187688	+	0.982229i	$0.439901\pi$
$114$	28.5764	2.67642
$115$	2.43958	0.227492
$116$	−10.6254	−0.986545
$117$	−2.58771	−0.239234
$118$	13.6665	1.25811
$119$	6.27501	0.575229
$120$	−2.54495	−0.232321
$121$	−9.60971	−0.873610
$122$	−12.4047	−1.12307
$123$	−5.98533	−0.539679
$124$	8.38400	0.752906
$125$	−1.00000	−0.0894427
$126$	−1.08312	−0.0964918
$127$	−11.0601	−0.981425	−0.490713	−	0.871322i	$-0.663263\pi$
$127$	−11.0601	−0.981425	−0.490713	+	0.871322i	$0.663263\pi$
$128$	9.98927	0.882935
$129$	8.85880	0.779974
$130$	7.78085	0.682425
$131$	4.37968	0.382654	0.191327	−	0.981526i	$-0.438721\pi$
$131$	4.37968	0.382654	0.191327	+	0.981526i	$0.438721\pi$
$132$	2.81171	0.244728
$133$	8.34549	0.723645
$134$	−16.7152	−1.44397
$135$	−4.55345	−0.391899
$136$	8.41649	0.721708
$137$	20.5760	1.75793	0.878965	−	0.476887i	$-0.158235\pi$
$137$	20.5760	1.75793	0.878965	+	0.476887i	$0.158235\pi$
$138$	8.35353	0.711100
$139$	−19.6350	−1.66542	−0.832708	−	0.553712i	$-0.813211\pi$
$139$	−19.6350	−1.66542	−0.832708	+	0.553712i	$0.813211\pi$
$140$	1.25677	0.106216
$141$	−20.3760	−1.71596
$142$	−7.26405	−0.609585
$143$	5.08377	0.425126
$144$	−2.96133	−0.246778
$145$	8.45454	0.702111
$146$	−14.7547	−1.22111
$147$	−1.89741	−0.156496
$148$	−10.4965	−0.862811
$149$	−16.1204	−1.32064	−0.660318	−	0.750986i	$-0.729579\pi$
$149$	−16.1204	−1.32064	−0.660318	+	0.750986i	$0.729579\pi$
$150$	−3.42417	−0.279583
$151$	−2.89920	−0.235933	−0.117967	−	0.993018i	$-0.537638\pi$
$151$	−2.89920	−0.235933	−0.117967	+	0.993018i	$0.537638\pi$
$152$	11.1936	0.907918
$153$	−3.76614	−0.304474
$154$	2.12787	0.171469
$155$	−6.67107	−0.535833
$156$	10.2814	0.823169
$157$	−17.8860	−1.42746	−0.713728	−	0.700423i	$-0.752995\pi$
$157$	−17.8860	−1.42746	−0.713728	+	0.700423i	$0.752995\pi$
$158$	−27.2092	−2.16465
$159$	−10.7642	−0.853656
$160$	6.22174	0.491871
$161$	2.43958	0.192266
$162$	−18.8412	−1.48030
$163$	19.0007	1.48825	0.744123	−	0.668042i	$-0.232867\pi$
$163$	19.0007	1.48825	0.744123	+	0.668042i	$0.232867\pi$
$164$	3.96444	0.309571
$165$	−2.23725	−0.174170
$166$	30.4444	2.36294
$167$	−23.3364	−1.80582	−0.902912	−	0.429824i	$-0.858575\pi$
$167$	−23.3364	−1.80582	−0.902912	+	0.429824i	$0.858575\pi$
$168$	−2.54495	−0.196347
$169$	5.58945	0.429958
$170$	11.3242	0.868527
$171$	−5.00880	−0.383033
$172$	−5.86771	−0.447409
$173$	−7.56837	−0.575412	−0.287706	−	0.957719i	$-0.592893\pi$
$173$	−7.56837	−0.575412	−0.287706	+	0.957719i	$0.592893\pi$
$174$	28.9498	2.19468
$175$	−1.00000	−0.0755929
$176$	5.81779	0.438532
$177$	−14.3690	−1.08004
$178$	−6.18877	−0.463868
$179$	−7.60210	−0.568208	−0.284104	−	0.958793i	$-0.591696\pi$
$179$	−7.60210	−0.568208	−0.284104	+	0.958793i	$0.591696\pi$
$180$	−0.754289	−0.0562214
$181$	−10.1245	−0.752552	−0.376276	−	0.926508i	$-0.622796\pi$
$181$	−10.1245	−0.752552	−0.376276	+	0.926508i	$0.622796\pi$
$182$	7.78085	0.576755
$183$	13.0424	0.964120
$184$	3.27213	0.241225
$185$	8.35200	0.614051
$186$	−22.8429	−1.67492
$187$	7.39889	0.541061
$188$	13.4962	0.984312
$189$	−4.55345	−0.331215
$190$	15.0607	1.09262
$191$	11.5722	0.837337	0.418669	−	0.908139i	$-0.362497\pi$
$191$	11.5722	0.837337	0.418669	+	0.908139i	$0.362497\pi$
$192$	2.58036	0.186221
$193$	10.4144	0.749642	0.374821	−	0.927097i	$-0.377704\pi$
$193$	10.4144	0.749642	0.374821	+	0.927097i	$0.377704\pi$
$194$	−12.6646	−0.909265
$195$	−8.18079	−0.585839
$196$	1.25677	0.0897693
$197$	4.42420	0.315211	0.157606	−	0.987502i	$-0.449623\pi$
$197$	4.42420	0.315211	0.157606	+	0.987502i	$0.449623\pi$
$198$	−1.27711	−0.0907603
$199$	14.6784	1.04052	0.520261	−	0.854008i	$-0.325835\pi$
$199$	14.6784	1.04052	0.520261	+	0.854008i	$0.325835\pi$
$200$	−1.34127	−0.0948422
$201$	17.5743	1.23960
$202$	17.5255	1.23309
$203$	8.45454	0.593392
$204$	14.9635	1.04765
$205$	−3.15447	−0.220318
$206$	26.6530	1.85700
$207$	−1.46419	−0.101768
$208$	21.2735	1.47505
$209$	9.84021	0.680661
$210$	−3.42417	−0.236290
$211$	−0.982999	−0.0676724	−0.0338362	−	0.999427i	$-0.510772\pi$
$211$	−0.982999	−0.0676724	−0.0338362	+	0.999427i	$0.510772\pi$
$212$	7.12976	0.489674
$213$	7.63743	0.523308
$214$	−6.94948	−0.475057
$215$	4.66888	0.318415
$216$	−6.10741	−0.415557
$217$	−6.67107	−0.452862
$218$	−29.3847	−1.99018
$219$	15.5131	1.04828
$220$	1.48186	0.0999073
$221$	27.0550	1.81992
$222$	28.5987	1.91942
$223$	−15.4909	−1.03734	−0.518672	−	0.854973i	$-0.673574\pi$
$223$	−15.4909	−1.03734	−0.518672	+	0.854973i	$0.673574\pi$
$224$	6.22174	0.415707
$225$	0.600181	0.0400121
$226$	7.20110	0.479010
$227$	−5.75599	−0.382038	−0.191019	−	0.981586i	$-0.561179\pi$
$227$	−5.75599	−0.382038	−0.191019	+	0.981586i	$0.561179\pi$
$228$	19.9008	1.31796
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.40259	0.290298
$231$	−2.23725	−0.147200
$232$	11.3398	0.744496
$233$	12.6523	0.828880	0.414440	−	0.910077i	$-0.363977\pi$
$233$	12.6523	0.828880	0.414440	+	0.910077i	$0.363977\pi$
$234$	−4.66992	−0.305282
$235$	−10.7388	−0.700522
$236$	9.51745	0.619533
$237$	28.6078	1.85827
$238$	11.3242	0.734039
$239$	−18.6702	−1.20768	−0.603838	−	0.797107i	$-0.706363\pi$
$239$	−18.6702	−1.20768	−0.603838	+	0.797107i	$0.706363\pi$
$240$	−9.36197	−0.604313
$241$	27.0449	1.74211	0.871057	−	0.491182i	$-0.163435\pi$
$241$	27.0449	1.74211	0.871057	+	0.491182i	$0.163435\pi$
$242$	−17.3422	−1.11480
$243$	6.14927	0.394476
$244$	−8.63873	−0.553038
$245$	−1.00000	−0.0638877
$246$	−10.8014	−0.688675
$247$	35.9820	2.28948
$248$	−8.94772	−0.568181
$249$	−32.0093	−2.02851
$250$	−1.80465	−0.114136
$251$	4.81484	0.303910	0.151955	−	0.988387i	$-0.451443\pi$
$251$	4.81484	0.303910	0.151955	+	0.988387i	$0.451443\pi$
$252$	−0.754289	−0.0475158
$253$	2.87652	0.180845
$254$	−19.9596	−1.25238
$255$	−11.9063	−0.745601
$256$	20.7470	1.29669
$257$	−10.4107	−0.649400	−0.324700	−	0.945817i	$-0.605263\pi$
$257$	−10.4107	−0.649400	−0.324700	+	0.945817i	$0.605263\pi$
$258$	15.9871	0.995310
$259$	8.35200	0.518968
$260$	5.41863	0.336049
$261$	−5.07425	−0.314088
$262$	7.90379	0.488298
$263$	−20.1531	−1.24269	−0.621346	−	0.783536i	$-0.713414\pi$
$263$	−20.1531	−1.24269	−0.621346	+	0.783536i	$0.713414\pi$
$264$	−3.00076	−0.184684
$265$	−5.67308	−0.348495
$266$	15.0607	0.923431
$267$	6.50689	0.398215
$268$	−11.6405	−0.711059
$269$	−15.7211	−0.958535	−0.479268	−	0.877669i	$-0.659098\pi$
$269$	−15.7211	−0.958535	−0.479268	+	0.877669i	$0.659098\pi$
$270$	−8.21740	−0.500095
$271$	17.4652	1.06093	0.530466	−	0.847706i	$-0.322017\pi$
$271$	17.4652	1.06093	0.530466	+	0.847706i	$0.322017\pi$
$272$	30.9613	1.87731
$273$	−8.18079	−0.495124
$274$	37.1326	2.24326
$275$	−1.17911	−0.0711027
$276$	5.81745	0.350169
$277$	19.0232	1.14299	0.571497	−	0.820604i	$-0.306363\pi$
$277$	19.0232	1.14299	0.571497	+	0.820604i	$0.306363\pi$
$278$	−35.4343	−2.12521
$279$	4.00385	0.239704
$280$	−1.34127	−0.0801563
$281$	−2.46876	−0.147274	−0.0736368	−	0.997285i	$-0.523461\pi$
$281$	−2.46876	−0.147274	−0.0736368	+	0.997285i	$0.523461\pi$
$282$	−36.7715	−2.18971
$283$	−21.5984	−1.28389	−0.641945	−	0.766751i	$-0.721872\pi$
$283$	−21.5984	−1.28389	−0.641945	+	0.766751i	$0.721872\pi$
$284$	−5.05872	−0.300180
$285$	−15.8348	−0.937975
$286$	9.17444	0.542496
$287$	−3.15447	−0.186202
$288$	−3.73417	−0.220038
$289$	22.3757	1.31622
$290$	15.2575	0.895951
$291$	13.3156	0.780573
$292$	−10.2753	−0.601315
$293$	21.4460	1.25289	0.626445	−	0.779466i	$-0.284509\pi$
$293$	21.4460	1.25289	0.626445	+	0.779466i	$0.284509\pi$
$294$	−3.42417	−0.199702
$295$	−7.57294	−0.440914
$296$	11.2023	0.651121
$297$	−5.36900	−0.311541
$298$	−29.0918	−1.68524
$299$	10.5183	0.608292
$300$	−2.38461	−0.137676
$301$	4.66888	0.269110
$302$	−5.23204	−0.301070
$303$	−18.4264	−1.05857
$304$	41.1772	2.36167
$305$	6.87376	0.393590
$306$	−6.79657	−0.388534
$307$	1.74161	0.0993991	0.0496996	−	0.998764i	$-0.484174\pi$
$307$	1.74161	0.0993991	0.0496996	+	0.998764i	$0.484174\pi$
$308$	1.48186	0.0844370
$309$	−28.0230	−1.59417
$310$	−12.0390	−0.683767
$311$	−26.0742	−1.47853	−0.739266	−	0.673414i	$-0.764827\pi$
$311$	−26.0742	−1.47853	−0.739266	+	0.673414i	$0.764827\pi$
$312$	−10.9727	−0.621205
$313$	18.8528	1.06562	0.532811	−	0.846234i	$-0.321136\pi$
$313$	18.8528	1.06562	0.532811	+	0.846234i	$0.321136\pi$
$314$	−32.2779	−1.82155
$315$	0.600181	0.0338164
$316$	−18.9486	−1.06594
$317$	−4.29458	−0.241208	−0.120604	−	0.992701i	$-0.538483\pi$
$317$	−4.29458	−0.241208	−0.120604	+	0.992701i	$0.538483\pi$
$318$	−19.4256	−1.08933
$319$	9.96879	0.558145
$320$	1.35993	0.0760225
$321$	7.30670	0.407820
$322$	4.40259	0.245347
$323$	52.3680	2.91383
$324$	−13.1211	−0.728949
$325$	−4.31155	−0.239162
$326$	34.2896	1.89912
$327$	30.8951	1.70850
$328$	−4.23100	−0.233618
$329$	−10.7388	−0.592049
$330$	−4.03746	−0.222255
$331$	−33.1987	−1.82477	−0.912384	−	0.409336i	$-0.865760\pi$
$331$	−33.1987	−1.82477	−0.912384	+	0.409336i	$0.865760\pi$
$332$	21.2017	1.16359
$333$	−5.01271	−0.274695
$334$	−42.1141	−2.30438
$335$	9.26226	0.506051
$336$	−9.36197	−0.510738
$337$	−32.6322	−1.77759	−0.888796	−	0.458304i	$-0.848457\pi$
$337$	−32.6322	−1.77759	−0.888796	+	0.458304i	$0.848457\pi$
$338$	10.0870	0.548661
$339$	−7.57125	−0.411214
$340$	7.88624	0.427691
$341$	−7.86589	−0.425962
$342$	−9.03915	−0.488781
$343$	−1.00000	−0.0539949
$344$	6.26224	0.337637
$345$	−4.62889	−0.249211
$346$	−13.6583	−0.734273
$347$	−5.77989	−0.310281	−0.155140	−	0.987892i	$-0.549583\pi$
$347$	−5.77989	−0.310281	−0.155140	+	0.987892i	$0.549583\pi$
$348$	20.1608	1.08073
$349$	−9.46667	−0.506739	−0.253370	−	0.967370i	$-0.581539\pi$
$349$	−9.46667	−0.506739	−0.253370	+	0.967370i	$0.581539\pi$
$350$	−1.80465	−0.0964627
$351$	−19.6324	−1.04790
$352$	7.33608	0.391014
$353$	−26.0073	−1.38423	−0.692113	−	0.721789i	$-0.743320\pi$
$353$	−26.0073	−1.38423	−0.692113	+	0.721789i	$0.743320\pi$
$354$	−25.9311	−1.37822
$355$	4.02518	0.213634
$356$	−4.30990	−0.228424
$357$	−11.9063	−0.630147
$358$	−13.7192	−0.725080
$359$	−8.74886	−0.461747	−0.230874	−	0.972984i	$-0.574158\pi$
$359$	−8.74886	−0.461747	−0.230874	+	0.972984i	$0.574158\pi$
$360$	0.805006	0.0424275
$361$	50.6471	2.66564
$362$	−18.2713	−0.960318
$363$	18.2336	0.957016
$364$	5.41863	0.284013
$365$	8.17594	0.427948
$366$	23.5369	1.23030
$367$	19.6223	1.02428	0.512138	−	0.858903i	$-0.328854\pi$
$367$	19.6223	1.02428	0.512138	+	0.858903i	$0.328854\pi$
$368$	12.0370	0.627474
$369$	1.89325	0.0985587
$370$	15.0725	0.783580
$371$	−5.67308	−0.294532
$372$	−15.9079	−0.824787
$373$	29.5822	1.53171	0.765853	−	0.643015i	$-0.222317\pi$
$373$	29.5822	1.53171	0.765853	+	0.643015i	$0.222317\pi$
$374$	13.3524	0.690438
$375$	1.89741	0.0979821
$376$	−14.4036	−0.742811
$377$	36.4522	1.87738
$378$	−8.21740	−0.422657
$379$	−4.34627	−0.223253	−0.111626	−	0.993750i	$-0.535606\pi$
$379$	−4.34627	−0.223253	−0.111626	+	0.993750i	$0.535606\pi$
$380$	10.4884	0.538041
$381$	20.9856	1.07512
$382$	20.8838	1.06851
$383$	−5.07998	−0.259575	−0.129787	−	0.991542i	$-0.541430\pi$
$383$	−5.07998	−0.259575	−0.129787	+	0.991542i	$0.541430\pi$
$384$	−18.9538	−0.967231
$385$	−1.17911	−0.0600928
$386$	18.7943	0.956605
$387$	−2.80217	−0.142442
$388$	−8.81970	−0.447752
$389$	−22.0334	−1.11714	−0.558568	−	0.829459i	$-0.688649\pi$
$389$	−22.0334	−1.11714	−0.558568	+	0.829459i	$0.688649\pi$
$390$	−14.7635	−0.747578
$391$	15.3084	0.774177
$392$	−1.34127	−0.0677444
$393$	−8.31006	−0.419187
$394$	7.98414	0.402235
$395$	15.0772	0.758618
$396$	−0.889387	−0.0446934
$397$	2.42155	0.121534	0.0607670	−	0.998152i	$-0.480645\pi$
$397$	2.42155	0.121534	0.0607670	+	0.998152i	$0.480645\pi$
$398$	26.4893	1.32779
$399$	−15.8348	−0.792734
$400$	−4.93407	−0.246703
$401$	38.0656	1.90090	0.950452	−	0.310872i	$-0.100621\pi$
$401$	38.0656	1.90090	0.950452	+	0.310872i	$0.100621\pi$
$402$	31.7156	1.58183
$403$	−28.7626	−1.43277
$404$	12.2049	0.607216
$405$	10.4403	0.518784
$406$	15.2575	0.757217
$407$	9.84789	0.488142
$408$	−15.9696	−0.790611
$409$	3.51772	0.173940	0.0869701	−	0.996211i	$-0.472282\pi$
$409$	3.51772	0.173940	0.0869701	+	0.996211i	$0.472282\pi$
$410$	−5.69272	−0.281143
$411$	−39.0413	−1.92576
$412$	18.5613	0.914451
$413$	−7.57294	−0.372640
$414$	−2.64235	−0.129864
$415$	−16.8700	−0.828113
$416$	26.8253	1.31522
$417$	37.2557	1.82442
$418$	17.7581	0.868579
$419$	3.41851	0.167005	0.0835025	−	0.996508i	$-0.473389\pi$
$419$	3.41851	0.167005	0.0835025	+	0.996508i	$0.473389\pi$
$420$	−2.38461	−0.116357
$421$	9.10984	0.443986	0.221993	−	0.975048i	$-0.428744\pi$
$421$	9.10984	0.443986	0.221993	+	0.975048i	$0.428744\pi$
$422$	−1.77397	−0.0863556
$423$	6.44522	0.313377
$424$	−7.60915	−0.369533
$425$	−6.27501	−0.304382
$426$	13.7829	0.667784
$427$	6.87376	0.332644
$428$	−4.83966	−0.233934
$429$	−9.64602	−0.465714
$430$	8.42571	0.406324
$431$	−11.4372	−0.550909	−0.275454	−	0.961314i	$-0.588828\pi$
$431$	−11.4372	−0.550909	−0.275454	+	0.961314i	$0.588828\pi$
$432$	−22.4670	−1.08095
$433$	21.1673	1.01724	0.508618	−	0.860992i	$-0.330157\pi$
$433$	21.1673	1.01724	0.508618	+	0.860992i	$0.330157\pi$
$434$	−12.0390	−0.577889
$435$	−16.0418	−0.769144
$436$	−20.4636	−0.980031
$437$	20.3594	0.973924
$438$	27.9958	1.33769
$439$	34.1256	1.62873	0.814363	−	0.580355i	$-0.197086\pi$
$439$	34.1256	1.62873	0.814363	+	0.580355i	$0.197086\pi$
$440$	−1.58150	−0.0753951
$441$	0.600181	0.0285800
$442$	48.8249	2.32236
$443$	−11.4697	−0.544940	−0.272470	−	0.962164i	$-0.587841\pi$
$443$	−11.4697	−0.544940	−0.272470	+	0.962164i	$0.587841\pi$
$444$	19.9163	0.945186
$445$	3.42934	0.162566
$446$	−27.9556	−1.32374
$447$	30.5871	1.44672
$448$	1.35993	0.0642508
$449$	−24.4493	−1.15383	−0.576917	−	0.816803i	$-0.695744\pi$
$449$	−24.4493	−1.15383	−0.576917	+	0.816803i	$0.695744\pi$
$450$	1.08312	0.0510587
$451$	−3.71945	−0.175142
$452$	5.01489	0.235880
$453$	5.50098	0.258458
$454$	−10.3876	−0.487512
$455$	−4.31155	−0.202129
$456$	−21.2388	−0.994599
$457$	0.719906	0.0336758	0.0168379	−	0.999858i	$-0.494640\pi$
$457$	0.719906	0.0336758	0.0168379	+	0.999858i	$0.494640\pi$
$458$	1.80465	0.0843259
$459$	−28.5729	−1.33367
$460$	3.06599	0.142952
$461$	−22.2097	−1.03441	−0.517204	−	0.855862i	$-0.673027\pi$
$461$	−22.2097	−1.03441	−0.517204	+	0.855862i	$0.673027\pi$
$462$	−4.03746	−0.187840
$463$	34.0802	1.58384	0.791920	−	0.610625i	$-0.209082\pi$
$463$	34.0802	1.58384	0.791920	+	0.610625i	$0.209082\pi$
$464$	41.7153	1.93658
$465$	12.6578	0.586991
$466$	22.8330	1.05772
$467$	25.2207	1.16707	0.583537	−	0.812086i	$-0.301668\pi$
$467$	25.2207	1.16707	0.583537	+	0.812086i	$0.301668\pi$
$468$	−3.25216	−0.150331
$469$	9.26226	0.427692
$470$	−19.3798	−0.893924
$471$	33.9371	1.56374
$472$	−10.1574	−0.467531
$473$	5.50510	0.253125
$474$	51.6271	2.37131
$475$	−8.34549	−0.382917
$476$	7.88624	0.361465
$477$	3.40488	0.155899
$478$	−33.6932	−1.54109
$479$	−7.82653	−0.357603	−0.178802	−	0.983885i	$-0.557222\pi$
$479$	−7.82653	−0.357603	−0.178802	+	0.983885i	$0.557222\pi$
$480$	−11.8052	−0.538832
$481$	36.0101	1.64192
$482$	48.8066	2.22308
$483$	−4.62889	−0.210622
$484$	−12.0772	−0.548964
$485$	7.01775	0.318660
$486$	11.0973	0.503384
$487$	20.0572	0.908879	0.454440	−	0.890778i	$-0.349840\pi$
$487$	20.0572	0.908879	0.454440	+	0.890778i	$0.349840\pi$
$488$	9.21958	0.417351
$489$	−36.0521	−1.63033
$490$	−1.80465	−0.0815259
$491$	−18.2503	−0.823624	−0.411812	−	0.911269i	$-0.635104\pi$
$491$	−18.2503	−0.823624	−0.411812	+	0.911269i	$0.635104\pi$
$492$	−7.52218	−0.339126
$493$	53.0523	2.38935
$494$	64.9349	2.92156
$495$	0.707676	0.0318077
$496$	−32.9155	−1.47795
$497$	4.02518	0.180554
$498$	−57.7656	−2.58854
$499$	−9.98776	−0.447113	−0.223557	−	0.974691i	$-0.571767\pi$
$499$	−9.98776	−0.447113	−0.223557	+	0.974691i	$0.571767\pi$
$500$	−1.25677	−0.0562045
$501$	44.2788	1.97823
$502$	8.68911	0.387814
$503$	−19.0253	−0.848294	−0.424147	−	0.905593i	$-0.639426\pi$
$503$	−19.0253	−0.848294	−0.424147	+	0.905593i	$0.639426\pi$
$504$	0.805006	0.0358578
$505$	−9.71131	−0.432148
$506$	5.19111	0.230773
$507$	−10.6055	−0.471007
$508$	−13.9000	−0.616713
$509$	−25.5640	−1.13310	−0.566552	−	0.824026i	$-0.691723\pi$
$509$	−25.5640	−1.13310	−0.566552	+	0.824026i	$0.691723\pi$
$510$	−21.4867	−0.951447
$511$	8.17594	0.361682
$512$	17.4626	0.771746
$513$	−38.0008	−1.67777
$514$	−18.7876	−0.828687
$515$	−14.7691	−0.650803
$516$	11.1335	0.490124
$517$	−12.6622	−0.556882
$518$	15.0725	0.662246
$519$	14.3603	0.630348
$520$	−5.78296	−0.253599
$521$	−4.60081	−0.201565	−0.100783	−	0.994908i	$-0.532135\pi$
$521$	−4.60081	−0.201565	−0.100783	+	0.994908i	$0.532135\pi$
$522$	−9.15726	−0.400802
$523$	−24.7295	−1.08135	−0.540673	−	0.841233i	$-0.681830\pi$
$523$	−24.7295	−1.08135	−0.540673	+	0.841233i	$0.681830\pi$
$524$	5.50425	0.240454
$525$	1.89741	0.0828099
$526$	−36.3693	−1.58578
$527$	−41.8610	−1.82349
$528$	−11.0388	−0.480400
$529$	−17.0485	−0.741238
$530$	−10.2379	−0.444708
$531$	4.54514	0.197242
$532$	10.4884	0.454728
$533$	−13.6006	−0.589109
$534$	11.7427	0.508155
$535$	3.85087	0.166488
$536$	12.4232	0.536601
$537$	14.4243	0.622456
$538$	−28.3712	−1.22317
$539$	−1.17911	−0.0507877
$540$	−5.72264	−0.246263
$541$	−8.17373	−0.351416	−0.175708	−	0.984442i	$-0.556221\pi$
$541$	−8.17373	−0.351416	−0.175708	+	0.984442i	$0.556221\pi$
$542$	31.5185	1.35384
$543$	19.2105	0.824400
$544$	39.0414	1.67389
$545$	16.2827	0.697475
$546$	−14.7635	−0.631819
$547$	−16.3200	−0.697794	−0.348897	−	0.937161i	$-0.613444\pi$
$547$	−16.3200	−0.697794	−0.348897	+	0.937161i	$0.613444\pi$
$548$	25.8594	1.10466
$549$	−4.12550	−0.176072
$550$	−2.12787	−0.0907329
$551$	70.5572	3.00584
$552$	−6.20859	−0.264255
$553$	15.0772	0.641149
$554$	34.3303	1.45855
$555$	−15.8472	−0.672677
$556$	−24.6766	−1.04652
$557$	−19.5320	−0.827596	−0.413798	−	0.910369i	$-0.635798\pi$
$557$	−19.5320	−0.827596	−0.413798	+	0.910369i	$0.635798\pi$
$558$	7.22556	0.305882
$559$	20.1301	0.851413
$560$	−4.93407	−0.208502
$561$	−14.0388	−0.592717
$562$	−4.45525	−0.187933
$563$	14.4725	0.609942	0.304971	−	0.952362i	$-0.401353\pi$
$563$	14.4725	0.609942	0.304971	+	0.952362i	$0.401353\pi$
$564$	−25.6079	−1.07829
$565$	−3.99030	−0.167873
$566$	−38.9775	−1.63835
$567$	10.4403	0.438452
$568$	5.39886	0.226531
$569$	21.2094	0.889144	0.444572	−	0.895743i	$-0.353356\pi$
$569$	21.2094	0.889144	0.444572	+	0.895743i	$0.353356\pi$
$570$	−28.5764	−1.19693
$571$	−23.9805	−1.00355	−0.501776	−	0.864998i	$-0.667320\pi$
$571$	−23.9805	−1.00355	−0.501776	+	0.864998i	$0.667320\pi$
$572$	6.38913	0.267143
$573$	−21.9573	−0.917280
$574$	−5.69272	−0.237609
$575$	−2.43958	−0.101737
$576$	−0.816206	−0.0340086
$577$	−18.4212	−0.766883	−0.383442	−	0.923565i	$-0.625261\pi$
$577$	−18.4212	−0.766883	−0.383442	+	0.923565i	$0.625261\pi$
$578$	40.3804	1.67960
$579$	−19.7604	−0.821213
$580$	10.6254	0.441196
$581$	−16.8700	−0.699884
$582$	24.0300	0.996075
$583$	−6.68916	−0.277037
$584$	10.9662	0.453783
$585$	2.58771	0.106989
$586$	38.7026	1.59879
$587$	−11.6032	−0.478914	−0.239457	−	0.970907i	$-0.576969\pi$
$587$	−11.6032	−0.478914	−0.239457	+	0.970907i	$0.576969\pi$
$588$	−2.38461	−0.0983398
$589$	−55.6733	−2.29398
$590$	−13.6665	−0.562642
$591$	−8.39454	−0.345305
$592$	41.2094	1.69369
$593$	6.19360	0.254341	0.127170	−	0.991881i	$-0.459410\pi$
$593$	6.19360	0.254341	0.127170	+	0.991881i	$0.459410\pi$
$594$	−9.68917	−0.397552
$595$	−6.27501	−0.257250
$596$	−20.2597	−0.829868
$597$	−27.8509	−1.13986
$598$	18.9820	0.776230
$599$	−12.5178	−0.511465	−0.255732	−	0.966748i	$-0.582317\pi$
$599$	−12.5178	−0.511465	−0.255732	+	0.966748i	$0.582317\pi$
$600$	2.54495	0.103897
$601$	−43.7326	−1.78389	−0.891945	−	0.452144i	$-0.850659\pi$
$601$	−43.7326	−1.78389	−0.891945	+	0.452144i	$0.850659\pi$
$602$	8.42571	0.343406
$603$	−5.55903	−0.226381
$604$	−3.64362	−0.148257
$605$	9.60971	0.390690
$606$	−33.2532	−1.35082
$607$	7.18883	0.291785	0.145893	−	0.989300i	$-0.453395\pi$
$607$	7.18883	0.291785	0.145893	+	0.989300i	$0.453395\pi$
$608$	51.9234	2.10577
$609$	−16.0418	−0.650045
$610$	12.4047	0.502253
$611$	−46.3009	−1.87313
$612$	−4.73317	−0.191327
$613$	−25.4911	−1.02958	−0.514788	−	0.857317i	$-0.672129\pi$
$613$	−25.4911	−1.02958	−0.514788	+	0.857317i	$0.672129\pi$
$614$	3.14301	0.126841
$615$	5.98533	0.241352
$616$	−1.58150	−0.0637205
$617$	7.08595	0.285269	0.142635	−	0.989775i	$-0.454443\pi$
$617$	7.08595	0.285269	0.142635	+	0.989775i	$0.454443\pi$
$618$	−50.5718	−2.03430
$619$	−12.4599	−0.500806	−0.250403	−	0.968142i	$-0.580563\pi$
$619$	−12.4599	−0.500806	−0.250403	+	0.968142i	$0.580563\pi$
$620$	−8.38400	−0.336710
$621$	−11.1085	−0.445768
$622$	−47.0548	−1.88673
$623$	3.42934	0.137394
$624$	−40.3646	−1.61588
$625$	1.00000	0.0400000
$626$	34.0227	1.35982
$627$	−18.6709	−0.745646
$628$	−22.4785	−0.896991
$629$	52.4089	2.08968
$630$	1.08312	0.0431525
$631$	−9.34565	−0.372044	−0.186022	−	0.982546i	$-0.559560\pi$
$631$	−9.34565	−0.372044	−0.186022	+	0.982546i	$0.559560\pi$
$632$	20.2227	0.804415
$633$	1.86516	0.0741333
$634$	−7.75023	−0.307801
$635$	11.0601	0.438907
$636$	−13.5281	−0.536425
$637$	−4.31155	−0.170830
$638$	17.9902	0.712239
$639$	−2.41584	−0.0955690
$640$	−9.98927	−0.394860
$641$	33.8535	1.33713	0.668567	−	0.743652i	$-0.266908\pi$
$641$	33.8535	1.33713	0.668567	+	0.743652i	$0.266908\pi$
$642$	13.1860	0.520412
$643$	−21.9663	−0.866268	−0.433134	−	0.901329i	$-0.642592\pi$
$643$	−21.9663	−0.866268	−0.433134	+	0.901329i	$0.642592\pi$
$644$	3.06599	0.120817
$645$	−8.85880	−0.348815
$646$	94.5060	3.71829
$647$	45.9565	1.80674	0.903368	−	0.428867i	$-0.141087\pi$
$647$	45.9565	1.80674	0.903368	+	0.428867i	$0.141087\pi$
$648$	14.0033	0.550102
$649$	−8.92930	−0.350506
$650$	−7.78085	−0.305190
$651$	12.6578	0.496098
$652$	23.8795	0.935192
$653$	35.2509	1.37947	0.689736	−	0.724061i	$-0.257726\pi$
$653$	35.2509	1.37947	0.689736	+	0.724061i	$0.257726\pi$
$654$	55.7549	2.18019
$655$	−4.37968	−0.171128
$656$	−15.5644	−0.607686
$657$	−4.90704	−0.191442
$658$	−19.3798	−0.755503
$659$	30.1615	1.17493	0.587463	−	0.809251i	$-0.300127\pi$
$659$	30.1615	1.17493	0.587463	+	0.809251i	$0.300127\pi$
$660$	−2.81171	−0.109446
$661$	−23.8616	−0.928110	−0.464055	−	0.885806i	$-0.653606\pi$
$661$	−23.8616	−0.928110	−0.464055	+	0.885806i	$0.653606\pi$
$662$	−59.9122	−2.32855
$663$	−51.3345	−1.99367
$664$	−22.6272	−0.878105
$665$	−8.34549	−0.323624
$666$	−9.04620	−0.350533
$667$	20.6255	0.798622
$668$	−29.3285	−1.13475
$669$	29.3926	1.13638
$670$	16.7152	0.645763
$671$	8.10488	0.312886
$672$	−11.8052	−0.455396
$673$	−22.5098	−0.867688	−0.433844	−	0.900988i	$-0.642843\pi$
$673$	−22.5098	−0.867688	−0.433844	+	0.900988i	$0.642843\pi$
$674$	−58.8898	−2.26835
$675$	4.55345	0.175262
$676$	7.02465	0.270179
$677$	29.4466	1.13172	0.565862	−	0.824500i	$-0.308543\pi$
$677$	29.4466	1.13172	0.565862	+	0.824500i	$0.308543\pi$
$678$	−13.6635	−0.524742
$679$	7.01775	0.269317
$680$	−8.41649	−0.322758
$681$	10.9215	0.418512
$682$	−14.1952	−0.543562
$683$	22.6563	0.866919	0.433460	−	0.901173i	$-0.357293\pi$
$683$	22.6563	0.866919	0.433460	+	0.901173i	$0.357293\pi$
$684$	−6.29491	−0.240692
$685$	−20.5760	−0.786170
$686$	−1.80465	−0.0689019
$687$	−1.89741	−0.0723909
$688$	23.0366	0.878261
$689$	−24.4598	−0.931843
$690$	−8.35353	−0.318013
$691$	26.6414	1.01349	0.506744	−	0.862097i	$-0.330849\pi$
$691$	26.6414	1.01349	0.506744	+	0.862097i	$0.330849\pi$
$692$	−9.51170	−0.361580
$693$	0.707676	0.0268824
$694$	−10.4307	−0.395943
$695$	19.6350	0.744797
$696$	−21.5164	−0.815575
$697$	−19.7943	−0.749763
$698$	−17.0841	−0.646641
$699$	−24.0067	−0.908015
$700$	−1.25677	−0.0475014
$701$	−32.2092	−1.21652	−0.608262	−	0.793736i	$-0.708133\pi$
$701$	−32.2092	−1.21652	−0.608262	+	0.793736i	$0.708133\pi$
$702$	−35.4297	−1.33721
$703$	69.7015	2.62884
$704$	1.60350	0.0604343
$705$	20.3760	0.767403
$706$	−46.9341	−1.76639
$707$	−9.71131	−0.365232
$708$	−18.0585	−0.678682
$709$	19.4894	0.731938	0.365969	−	0.930627i	$-0.380738\pi$
$709$	19.4894	0.731938	0.365969	+	0.930627i	$0.380738\pi$
$710$	7.26405	0.272615
$711$	−9.04907	−0.339367
$712$	4.59968	0.172380
$713$	−16.2746	−0.609488
$714$	−21.4867	−0.804120
$715$	−5.08377	−0.190122
$716$	−9.55410	−0.357053
$717$	35.4251	1.32298
$718$	−15.7887	−0.589227
$719$	−7.42710	−0.276984	−0.138492	−	0.990364i	$-0.544226\pi$
$719$	−7.42710	−0.276984	−0.138492	+	0.990364i	$0.544226\pi$
$720$	2.96133	0.110362
$721$	−14.7691	−0.550029
$722$	91.4005	3.40157
$723$	−51.3153	−1.90844
$724$	−12.7242	−0.472892
$725$	−8.45454	−0.313994
$726$	32.9053	1.22123
$727$	−48.5065	−1.79901	−0.899503	−	0.436915i	$-0.856071\pi$
$727$	−48.5065	−1.79901	−0.899503	+	0.436915i	$0.856071\pi$
$728$	−5.78296	−0.214331
$729$	19.6533	0.727899
$730$	14.7547	0.546097
$731$	29.2972	1.08360
$732$	16.3913	0.605838
$733$	14.1021	0.520872	0.260436	−	0.965491i	$-0.416134\pi$
$733$	14.1021	0.520872	0.260436	+	0.965491i	$0.416134\pi$
$734$	35.4114	1.30706
$735$	1.89741	0.0699872
$736$	15.1784	0.559483
$737$	10.9212	0.402287
$738$	3.41666	0.125769
$739$	−29.3210	−1.07859	−0.539296	−	0.842116i	$-0.681310\pi$
$739$	−29.3210	−1.07859	−0.539296	+	0.842116i	$0.681310\pi$
$740$	10.4965	0.385861
$741$	−68.2727	−2.50806
$742$	−10.2379	−0.375847
$743$	−48.7566	−1.78871	−0.894353	−	0.447362i	$-0.852363\pi$
$743$	−48.7566	−1.78871	−0.894353	+	0.447362i	$0.852363\pi$
$744$	16.9775	0.622426
$745$	16.1204	0.590607
$746$	53.3855	1.95458
$747$	10.1250	0.370455
$748$	9.29871	0.339994
$749$	3.85087	0.140708
$750$	3.42417	0.125033
$751$	−34.2348	−1.24925	−0.624623	−	0.780926i	$-0.714748\pi$
$751$	−34.2348	−1.24925	−0.624623	+	0.780926i	$0.714748\pi$
$752$	−52.9860	−1.93220
$753$	−9.13574	−0.332925
$754$	65.7835	2.39569
$755$	2.89920	0.105513
$756$	−5.72264	−0.208130
$757$	−26.8171	−0.974683	−0.487341	−	0.873212i	$-0.662033\pi$
$757$	−26.8171	−0.974683	−0.487341	+	0.873212i	$0.662033\pi$
$758$	−7.84350	−0.284889
$759$	−5.45794	−0.198111
$760$	−11.1936	−0.406033
$761$	−49.7758	−1.80437	−0.902186	−	0.431347i	$-0.858038\pi$
$761$	−49.7758	−1.80437	−0.902186	+	0.431347i	$0.858038\pi$
$762$	37.8717	1.37195
$763$	16.2827	0.589474
$764$	14.5436	0.526170
$765$	3.76614	0.136165
$766$	−9.16760	−0.331239
$767$	−32.6511	−1.17896
$768$	−39.3657	−1.42049
$769$	11.6586	0.420419	0.210210	−	0.977656i	$-0.432585\pi$
$769$	11.6586	0.420419	0.210210	+	0.977656i	$0.432585\pi$
$770$	−2.12787	−0.0766833
$771$	19.7534	0.711400
$772$	13.0885	0.471064
$773$	−3.98512	−0.143335	−0.0716674	−	0.997429i	$-0.522832\pi$
$773$	−3.98512	−0.143335	−0.0716674	+	0.997429i	$0.522832\pi$
$774$	−5.05695	−0.181768
$775$	6.67107	0.239632
$776$	9.41271	0.337897
$777$	−15.8472	−0.568515
$778$	−39.7626	−1.42556
$779$	−26.3256	−0.943211
$780$	−10.2814	−0.368132
$781$	4.74611	0.169829
$782$	27.6263	0.987913
$783$	−38.4973	−1.37578
$784$	−4.93407	−0.176217
$785$	17.8860	0.638377
$786$	−14.9968	−0.534917
$787$	8.63861	0.307933	0.153967	−	0.988076i	$-0.450795\pi$
$787$	8.63861	0.307933	0.153967	+	0.988076i	$0.450795\pi$
$788$	5.56020	0.198074
$789$	38.2387	1.36133
$790$	27.2092	0.968059
$791$	−3.99030	−0.141879
$792$	0.949186	0.0337279
$793$	29.6365	1.05242
$794$	4.37005	0.155087
$795$	10.7642	0.381767
$796$	18.4473	0.653848
$797$	−26.4526	−0.937000	−0.468500	−	0.883463i	$-0.655205\pi$
$797$	−26.4526	−0.937000	−0.468500	+	0.883463i	$0.655205\pi$
$798$	−28.5764	−1.01159
$799$	−67.3860	−2.38395
$800$	−6.22174	−0.219972
$801$	−2.05823	−0.0727239
$802$	68.6951	2.42571
$803$	9.64029	0.340198
$804$	22.0869	0.778945
$805$	−2.43958	−0.0859837
$806$	−51.9066	−1.82833
$807$	29.8295	1.05005
$808$	−13.0255	−0.458236
$809$	13.4552	0.473059	0.236530	−	0.971624i	$-0.423990\pi$
$809$	13.4552	0.473059	0.236530	+	0.971624i	$0.423990\pi$
$810$	18.8412	0.662011
$811$	13.0283	0.457485	0.228743	−	0.973487i	$-0.426539\pi$
$811$	13.0283	0.457485	0.228743	+	0.973487i	$0.426539\pi$
$812$	10.6254	0.372879
$813$	−33.1386	−1.16222
$814$	17.7720	0.622909
$815$	−19.0007	−0.665564
$816$	−58.7464	−2.05654
$817$	38.9641	1.36318
$818$	6.34827	0.221962
$819$	2.58771	0.0904219
$820$	−3.96444	−0.138444
$821$	−12.1738	−0.424868	−0.212434	−	0.977175i	$-0.568139\pi$
$821$	−12.1738	−0.424868	−0.212434	+	0.977175i	$0.568139\pi$
$822$	−70.4559	−2.45743
$823$	−17.4314	−0.607622	−0.303811	−	0.952732i	$-0.598259\pi$
$823$	−17.4314	−0.607622	−0.303811	+	0.952732i	$0.598259\pi$
$824$	−19.8093	−0.690091
$825$	2.23725	0.0778911
$826$	−13.6665	−0.475519
$827$	−9.93135	−0.345347	−0.172673	−	0.984979i	$-0.555241\pi$
$827$	−9.93135	−0.345347	−0.172673	+	0.984979i	$0.555241\pi$
$828$	−1.84015	−0.0639495
$829$	22.5240	0.782289	0.391145	−	0.920329i	$-0.372079\pi$
$829$	22.5240	0.782289	0.391145	+	0.920329i	$0.372079\pi$
$830$	−30.4444	−1.05674
$831$	−36.0949	−1.25212
$832$	5.86342	0.203277
$833$	−6.27501	−0.217416
$834$	67.2335	2.32811
$835$	23.3364	0.807589
$836$	12.3669	0.427717
$837$	30.3764	1.04996
$838$	6.16922	0.213112
$839$	16.4303	0.567238	0.283619	−	0.958937i	$-0.408465\pi$
$839$	16.4303	0.567238	0.283619	+	0.958937i	$0.408465\pi$
$840$	2.54495	0.0878090
$841$	42.4792	1.46480
$842$	16.4401	0.566563
$843$	4.68425	0.161334
$844$	−1.23540	−0.0425243
$845$	−5.58945	−0.192283
$846$	11.6314	0.399895
$847$	9.60971	0.330194
$848$	−27.9914	−0.961228
$849$	40.9810	1.40647
$850$	−11.3242	−0.388417
$851$	20.3753	0.698458
$852$	9.59850	0.328839
$853$	27.8299	0.952879	0.476439	−	0.879207i	$-0.341927\pi$
$853$	27.8299	0.952879	0.476439	+	0.879207i	$0.341927\pi$
$854$	12.4047	0.424482
$855$	5.00880	0.171297
$856$	5.16506	0.176538
$857$	−53.5957	−1.83080	−0.915398	−	0.402551i	$-0.868124\pi$
$857$	−53.5957	−1.83080	−0.915398	+	0.402551i	$0.868124\pi$
$858$	−17.4077	−0.594289
$859$	−13.7286	−0.468413	−0.234206	−	0.972187i	$-0.575249\pi$
$859$	−13.7286	−0.468413	−0.234206	+	0.972187i	$0.575249\pi$
$860$	5.86771	0.200087
$861$	5.98533	0.203980
$862$	−20.6401	−0.703005
$863$	−45.6596	−1.55427	−0.777135	−	0.629334i	$-0.783328\pi$
$863$	−45.6596	−1.55427	−0.777135	+	0.629334i	$0.783328\pi$
$864$	−28.3304	−0.963819
$865$	7.56837	0.257332
$866$	38.1996	1.29808
$867$	−42.4560	−1.44188
$868$	−8.38400	−0.284572
$869$	17.7776	0.603065
$870$	−28.9498	−0.981490
$871$	39.9347	1.35314
$872$	21.8396	0.739581
$873$	−4.21192	−0.142552
$874$	36.7417	1.24281
$875$	1.00000	0.0338062
$876$	19.4964	0.658724
$877$	21.1754	0.715043	0.357522	−	0.933905i	$-0.383622\pi$
$877$	21.1754	0.715043	0.357522	+	0.933905i	$0.383622\pi$
$878$	61.5849	2.07839
$879$	−40.6920	−1.37251
$880$	−5.81779	−0.196118
$881$	18.3941	0.619712	0.309856	−	0.950783i	$-0.399719\pi$
$881$	18.3941	0.619712	0.309856	+	0.950783i	$0.399719\pi$
$882$	1.08312	0.0364705
$883$	−12.2328	−0.411666	−0.205833	−	0.978587i	$-0.565990\pi$
$883$	−12.2328	−0.411666	−0.205833	+	0.978587i	$0.565990\pi$
$884$	34.0019	1.14361
$885$	14.3690	0.483009
$886$	−20.6987	−0.695388
$887$	−12.4677	−0.418624	−0.209312	−	0.977849i	$-0.567122\pi$
$887$	−12.4677	−0.418624	−0.209312	+	0.977849i	$0.567122\pi$
$888$	−21.2554	−0.713285
$889$	11.0601	0.370944
$890$	6.18877	0.207448
$891$	12.3102	0.412409
$892$	−19.4684	−0.651852
$893$	−89.6205	−2.99904
$894$	55.1991	1.84613
$895$	7.60210	0.254110
$896$	−9.98927	−0.333718
$897$	−19.9577	−0.666367
$898$	−44.1225	−1.47239
$899$	−56.4008	−1.88107
$900$	0.754289	0.0251430
$901$	−35.5986	−1.18596
$902$	−6.71231	−0.223496
$903$	−8.85880	−0.294802
$904$	−5.35207	−0.178007
$905$	10.1245	0.336551
$906$	9.92735	0.329814
$907$	23.1146	0.767508	0.383754	−	0.923435i	$-0.374631\pi$
$907$	23.1146	0.767508	0.383754	+	0.923435i	$0.374631\pi$
$908$	−7.23395	−0.240067
$909$	5.82855	0.193321
$910$	−7.78085	−0.257933
$911$	−6.66096	−0.220687	−0.110344	−	0.993893i	$-0.535195\pi$
$911$	−6.66096	−0.220687	−0.110344	+	0.993893i	$0.535195\pi$
$912$	−78.1302	−2.58715
$913$	−19.8914	−0.658311
$914$	1.29918	0.0429730
$915$	−13.0424	−0.431167
$916$	1.25677	0.0415249
$917$	−4.37968	−0.144630
$918$	−51.5642	−1.70187
$919$	−5.43880	−0.179409	−0.0897047	−	0.995968i	$-0.528592\pi$
$919$	−5.43880	−0.179409	−0.0897047	+	0.995968i	$0.528592\pi$
$920$	−3.27213	−0.107879
$921$	−3.30456	−0.108889
$922$	−40.0807	−1.31999
$923$	17.3548	0.571239
$924$	−2.81171	−0.0924985
$925$	−8.35200	−0.274612
$926$	61.5028	2.02111
$927$	8.86411	0.291136
$928$	52.6019	1.72674
$929$	−35.6530	−1.16974	−0.584869	−	0.811128i	$-0.698854\pi$
$929$	−35.6530	−1.16974	−0.584869	+	0.811128i	$0.698854\pi$
$930$	22.8429	0.749048
$931$	−8.34549	−0.273512
$932$	15.9010	0.520856
$933$	49.4735	1.61969
$934$	45.5146	1.48928
$935$	−7.39889	−0.241970
$936$	3.47082	0.113447
$937$	−17.8279	−0.582413	−0.291207	−	0.956660i	$-0.594057\pi$
$937$	−17.8279	−0.582413	−0.291207	+	0.956660i	$0.594057\pi$
$938$	16.7152	0.545769
$939$	−35.7716	−1.16736
$940$	−13.4962	−0.440198
$941$	22.7426	0.741387	0.370693	−	0.928755i	$-0.379120\pi$
$941$	22.7426	0.741387	0.370693	+	0.928755i	$0.379120\pi$
$942$	61.2446	1.99546
$943$	−7.69556	−0.250602
$944$	−37.3654	−1.21614
$945$	4.55345	0.148124
$946$	9.93479	0.323008
$947$	−50.8578	−1.65266	−0.826328	−	0.563190i	$-0.809574\pi$
$947$	−50.8578	−1.65266	−0.826328	+	0.563190i	$0.809574\pi$
$948$	35.9534	1.16771
$949$	35.2509	1.14429
$950$	−15.0607	−0.488634
$951$	8.14861	0.264237
$952$	−8.41649	−0.272780
$953$	32.4333	1.05062	0.525309	−	0.850911i	$-0.323950\pi$
$953$	32.4333	1.05062	0.525309	+	0.850911i	$0.323950\pi$
$954$	6.14462	0.198939
$955$	−11.5722	−0.374469
$956$	−23.4642	−0.758885
$957$	−18.9149	−0.611433
$958$	−14.1242	−0.456331
$959$	−20.5760	−0.664435
$960$	−2.58036	−0.0832806
$961$	13.5032	0.435586
$962$	64.9856	2.09522
$963$	−2.31122	−0.0744780
$964$	33.9892	1.09472
$965$	−10.4144	−0.335250
$966$	−8.35353	−0.268770
$967$	−35.0683	−1.12772	−0.563860	−	0.825870i	$-0.690684\pi$
$967$	−35.0683	−1.12772	−0.563860	+	0.825870i	$0.690684\pi$
$968$	12.8892	0.414276
$969$	−99.3637	−3.19202
$970$	12.6646	0.406636
$971$	−38.9943	−1.25139	−0.625694	−	0.780069i	$-0.715184\pi$
$971$	−38.9943	−1.25139	−0.625694	+	0.780069i	$0.715184\pi$
$972$	7.72822	0.247883
$973$	19.6350	0.629468
$974$	36.1963	1.15980
$975$	8.18079	0.261995
$976$	33.9156	1.08561
$977$	−16.5406	−0.529181	−0.264591	−	0.964361i	$-0.585237\pi$
$977$	−16.5406	−0.529181	−0.264591	+	0.964361i	$0.585237\pi$
$978$	−65.0616	−2.08044
$979$	4.04356	0.129233
$980$	−1.25677	−0.0401460
$981$	−9.77258	−0.312015
$982$	−32.9354	−1.05101
$983$	−2.93120	−0.0934907	−0.0467453	−	0.998907i	$-0.514885\pi$
$983$	−2.93120	−0.0934907	−0.0467453	+	0.998907i	$0.514885\pi$
$984$	8.02795	0.255922
$985$	−4.42420	−0.140967
$986$	95.7409	3.04901
$987$	20.3760	0.648574
$988$	45.2211	1.43867
$989$	11.3901	0.362184
$990$	1.27711	0.0405892
$991$	14.2363	0.452233	0.226116	−	0.974100i	$-0.427397\pi$
$991$	14.2363	0.452233	0.226116	+	0.974100i	$0.427397\pi$
$992$	−41.5056	−1.31781
$993$	62.9918	1.99898
$994$	7.26405	0.230402
$995$	−14.6784	−0.465335
$996$	−40.2283	−1.27468
$997$	27.4134	0.868190	0.434095	−	0.900867i	$-0.357068\pi$
$997$	27.4134	0.868190	0.434095	+	0.900867i	$0.357068\pi$
$998$	−18.0244	−0.570553
$999$	−38.0304	−1.20323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.48	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.48	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} +O(q^{10})\)	\(q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} -1.80465 q^{10} -1.17911 q^{11} -2.38461 q^{12} -4.31155 q^{13} -1.80465 q^{14} +1.89741 q^{15} -4.93407 q^{16} -6.27501 q^{17} +1.08312 q^{18} -8.34549 q^{19} -1.25677 q^{20} +1.89741 q^{21} -2.12787 q^{22} -2.43958 q^{23} +2.54495 q^{24} +1.00000 q^{25} -7.78085 q^{26} +4.55345 q^{27} -1.25677 q^{28} -8.45454 q^{29} +3.42417 q^{30} +6.67107 q^{31} -6.22174 q^{32} +2.23725 q^{33} -11.3242 q^{34} +1.00000 q^{35} +0.754289 q^{36} -8.35200 q^{37} -15.0607 q^{38} +8.18079 q^{39} +1.34127 q^{40} +3.15447 q^{41} +3.42417 q^{42} -4.66888 q^{43} -1.48186 q^{44} -0.600181 q^{45} -4.40259 q^{46} +10.7388 q^{47} +9.36197 q^{48} +1.00000 q^{49} +1.80465 q^{50} +11.9063 q^{51} -5.41863 q^{52} +5.67308 q^{53} +8.21740 q^{54} +1.17911 q^{55} +1.34127 q^{56} +15.8348 q^{57} -15.2575 q^{58} +7.57294 q^{59} +2.38461 q^{60} -6.87376 q^{61} +12.0390 q^{62} -0.600181 q^{63} -1.35993 q^{64} +4.31155 q^{65} +4.03746 q^{66} -9.26226 q^{67} -7.88624 q^{68} +4.62889 q^{69} +1.80465 q^{70} -4.02518 q^{71} -0.805006 q^{72} -8.17594 q^{73} -15.0725 q^{74} -1.89741 q^{75} -10.4884 q^{76} +1.17911 q^{77} +14.7635 q^{78} -15.0772 q^{79} +4.93407 q^{80} -10.4403 q^{81} +5.69272 q^{82} +16.8700 q^{83} +2.38461 q^{84} +6.27501 q^{85} -8.42571 q^{86} +16.0418 q^{87} +1.58150 q^{88} -3.42934 q^{89} -1.08312 q^{90} +4.31155 q^{91} -3.06599 q^{92} -12.6578 q^{93} +19.3798 q^{94} +8.34549 q^{95} +11.8052 q^{96} -7.01775 q^{97} +1.80465 q^{98} -0.707676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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